{"title":"不包含小次的图的同构检验","authors":"Martin Grohe, Daniel Neuen, Daniel Wiebking","doi":"10.1137/21m1401930","DOIUrl":null,"url":null,"abstract":"We prove that there is a graph isomorphism test running in time $n^{\\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\\operatorname{poly}(h)}$ (Ponomarenko, 1988) and $n^{\\operatorname{polylog}(n)}$ (Babai, STOC 2016). For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Isomorphism Testing for Graphs Excluding Small Minors\",\"authors\":\"Martin Grohe, Daniel Neuen, Daniel Wiebking\",\"doi\":\"10.1137/21m1401930\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that there is a graph isomorphism test running in time $n^{\\\\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\\\\operatorname{poly}(h)}$ (Ponomarenko, 1988) and $n^{\\\\operatorname{polylog}(n)}$ (Babai, STOC 2016). For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments.\",\"PeriodicalId\":49532,\"journal\":{\"name\":\"SIAM Journal on Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/21m1401930\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/21m1401930","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
摘要
我们证明了在$n^{\operatorname{polylog}(h)}$ n -顶点图上存在一个图同构测试，该测试在$n^{\operatorname{polylog}}$上运行，不包括$h$顶点图作为次要图。以前已知的边界是$n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988)和$n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016)。对于该算法，我们将群论图同构机制的最新进展与新的图论论证结合起来。
Isomorphism Testing for Graphs Excluding Small Minors
We prove that there is a graph isomorphism test running in time $n^{\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988) and $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016). For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments.
期刊介绍：
The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.
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